--- a/sbin/update-ca-certificates
+++ b/sbin/update-ca-certificates
@@ -81,8 +81,8 @@ trap cleanup 0
 # Helper files.  (Some of them are not simple arrays because we spawn
 # subshells later on.)
 TEMPBUNDLE="${ETCCERTSDIR}/${CERTBUNDLE}.new"
-ADDED="$(mktemp -p "${TMPDIR:-/tmp}" "ca-certificates.tmp.XXXXXX")"
-REMOVED="$(mktemp -p "${TMPDIR:-/tmp}" "ca-certificates.tmp.XXXXXX")"
+ADDED="$(mktemp -t ca-certificates.tmp)"
+REMOVED="$(mktemp -t ca-certificates.tmp)"
 
 # Adds a certificate to the list of trusted ones.  This includes a symlink
 # in /etc/ssl/certs to the certificate file and its inclusion into the
